Download The Virginia SOLS A.9 and A.10- Statistics A.9: The student, given a

The Virginia SOLS A.9 and A.10- Statistics
A.9: The student, given a set of data, will interpret variation in real-world contexts and
calculate and interpret mean absolute deviation, standard deviation and z-scores.
Essential Knowledge and Skills
The student will use problem-solving, mathematical communications, mathematical reasoning,
connections, and representations to:
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Analyze descriptive statistics to determine the implications for the real-world situations
from which the data is derived.
Given data, including data in a real-world context, calculate and interpret the mean
absolute deviation of a data set.
Given data, including data in a real-world context, calculate variance and standard
deviation of a data set and interpret the standard deviation.
Given data, including data in a real-world context, calculate and interpret z-scores for a
data set.
Explain ways in which standard deviation addresses dispersion by examining the formula
for standard variation.
Compare and contrast mean absolute deviation and standard deviation in a real-world
context.
Essential understandings
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Descriptive statistics may include measures of center and dispersion.
Variance, standard deviation, and mean absolute deviation measure the dispersion of the
data.
The sum of the deviations of data points from the mean of the data set is 0.
Standard deviation is expressed in the original units of measurement of the data.
Standard deviation addresses the dispersion of data about the mean.
Standard deviation is calculated by taking the square root of the variance.
The greater the value of the standard deviation, the further the data tend to be dispersed
from the mean.
For a data distribution with outliers, the mean absolute deviation may be a better
measure of dispersion than the standard deviation or the variance.
A z-score (standard score) is a measure of position derived from the mean and standard
deviation of data.
A z-score derived from a particular data value tells how many standard deviations that
data value is above or below the mean of the data set. It is positive if the data value lies
above the mean and negative if the data value lies below the mean.
Teachers should not require students to use data sets of more than 10 elements.
In Algebra 1, the z-score will be used to determine how many standard deviations an
element is above or below the mean of the data set. It can also be used to determine the
value of the element, given the z-score of an unknown element and the mean and the
standard deviation of a data set. The z-score has a positive value if the element lies
above the mean and a negative value is the element lies below the mean.
Examples:
1) The data set shown has a mean of 37 and a standard deviation of 6.3, rounded to the
nearest tenth. {26, 29, 32, 33, 35, 36, 37, 39, 40, 44, 45, 48}. How many of these data points
have a z-score greater than -0.6?
2) A data set has a mean of 68.42 and a standard deviation of 7.91. An element in this set is
57. What is the z-score for 57? Round the answer to the nearest hundredth?
3) This table shows data on the number of dollars raised during a fundraiser for four different
classes and for one student in each class.
Mean for Class
Jill
Kelli
Monroe
Tim
60
58
55
57
Number of Dollars Raised
Standard Deviation
for Class
11
12
13
10
Student’s z-score
1.8
2.1
1.4
2.5
Which of the four students raised the greatest number of dollars?
4) The data on the annual rainfall for 32 cities is summarized in this histogram.
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The mean amount of rainfall for these cities is 32.5 inches.
The standard deviation of the data is 4 inches.
On the histogram, identify each interval that may have data points within 1.5 standard
deviations of the mean.
5) Which data set has less variation (more consistency) in the number of people playing
basketball during April 1-14?
______________________
Why? _______________________________________________________________________
6) Which data set has more dispersion? ____________________________
7) The standard deviation of data set 2 is almost __________ the standard deviation of data
set 1, indicating that the elements of data set ______ are more spread out with respect to the
________.
8) When a data set has clear outliers, the outlying elements have a less affect on the
calculation of the ______________________________________________________________
than on the ___________________________________________________________________
9) How many elements are above the mean? _______________________
10) How many elements are below the mean? __________________________
11) How many elements fall within one standard deviation of the mean? __________________
A.10: The student will compare and contrast multiple univariate data sets, using box-andwhisker plots.
12)
13) Draw an accurate box-and-whisker plot for the given data below:
29 22 27 36 25 32 36 28 37 29 20 21 33 26 31 20 18
Find the following:
a) Lower Extreme: _____
b) Lower Quartile: _____
e) Upper Extreme: _____
f) Outlier(s)?: _____
c) Median: _____
g) Mean: _____
d) Upper Quartile: _____
h) Mode: _____ i) Range:____
j) Interquartile range: _____
k) Percent of data more than 32.5? ______
l) Percent less than 28? _____
m) Percent more than 21.5? _____